We need to find the radius of the sphere

Surface area = 4 * pi * r^2

113.04 = 4 * pi * r^2 divide both sides by 4 pi

113.04 / [ 4 pi] = r^2

√ [ 113.04/ [ 4pi] ] = r

So...the volume is given by

(4/3) pi * r^3

(4/3)pi * (√ [ 113.04/ [ 4pi] ])^3 =

35.97 pi in^3